A099953 a(n) = A076795(n) - 1.

0, 1, 4, 19, 124, 1069, 11464, 146599, 2173624, 36633049, 691362124, 14440672699, 330674815924, 8236528396549, 221694575073424, 6411977928702799, 198310761891213424, 6530970632654064049, 228174066109353835924

Offset: 1

Author

N. J. A. Sloane, Nov 12 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A001147.

Programs

Maple

a[1]:=0: a[2]:=1: for n from 3 to 30 do a[n]:=(2*n-2)*a[n-1]-(2*n-3)*a[n-2] od:seq(a[j],j=1..18); # Emeric Deutsch, Dec 20 2004

Mathematica

s = 0; lst = {s}; Do[s += n!!; AppendTo[lst, s], {n, 1, 32, 2}]; lst (* Zerinvary Lajos, Jul 13 2009 *)

Formula

a(n) = (2*n-2)*a(n-1)-(2*n-3)*a(n-2) with a(1)=0, a(2)=1. - Emeric Deutsch and Ira M. Gessel, Dec 19 2004

G.f.: A(x)=x/(1-x)/(U(0)-x), where U(k)= (2*k+1)*x + 1 - (2*k+3)*x/U(k+1); (continued fraction Euler's 1st kind, 1-step ). - Sergei N. Gladkovskii, Jun 27 2012

Extensions

More terms from Emeric Deutsch and Ira M. Gessel, Dec 20 2004